How often does he see her in person? What is their relationship and interaction like? Is there court-ordered visitation, and do both he and you stick to that schedule? If so, he may have to be content with that.
Does he have any idea what it takes to get a 4 year old to pay attention to anything, let alone a phone? Many parents and grandparents understand that kids don't want to talk every day on the phone, even to people they live with.
Without knowing the situation, I'd suggest that he at least FaceTime or Skype with her so there's a face for her to see. I like the idea below of him reading her a story. He could also read some stories onto a CD and you could play it anytime she asks or a couple of times per week at bedtime, and let him know you are doing this. The problem is, sometimes 4 year olds do better with picture books. Does he sing? He can sing some lullabies you can play at bedtime, or other songs for daytime.
Otherwise, you can consider putting the phone in front of her or putting her in front of the computer, and let him watch her get bored and run away to play. You make the effort to connect them, and then he's on his own.
I wouldn't turn it into a big fight to get her to sit still - that's a sure way to get her to resent him. Which is what you should tell him.
But again, without knowing more of the story, it's hard to say.